Ryan O'Donnell's Analysis of Boolean Functions PDF

Machine Theory

By Ryan O'Donnell

Boolean features are might be the main uncomplicated gadgets of research in theoretical laptop technology. in addition they come up in different parts of arithmetic, together with combinatorics, statistical physics, and mathematical social selection. the sphere of study of Boolean services seeks to appreciate them through their Fourier rework and different analytic equipment. this article offers a radical review of the sector, starting with the main easy definitions and continuing to complex subject matters reminiscent of hypercontractivity and isoperimetry. every one bankruptcy contains a 'highlight software' corresponding to Arrow's theorem from economics, the Goldreich–Levin set of rules from cryptography/learning idea, Håstad's NP-hardness of approximation effects, and 'sharp threshold' theorems for random graph homes. The e-book contains approximately 450 routines and will be used because the foundation of a one-semester graduate direction. it's going to entice complicated undergraduates, graduate scholars and researchers in laptop technological know-how conception and comparable mathematical fields.

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Analysis of Boolean Functions by Ryan O'Donnell

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